Hunter is the only player in NHL history to have more than 1,000 points (1,020; 323 goals, 697 assists) and 3,000 penalty minutes (3,565, second all-time to Dave Williams). Despite spending so much time in the penalty box, he ended his career with nine 20-goal seasons and six with at least 70 points.

The Quebec Nordiques selected Hunter in the second round (No. 41) of the 1979 NHL Draft after a 110-point season (42 goals, 68 assists) with Sudbury of the Ontario Hockey League. One year later, Hunter was in the NHL and finished his first season with 63 points (19 goals, 44 assists) in 80 games.

Hunter scored one of the most famous goals in Nordiques history on April 13, 1982, beating Rick Wamsley 22 seconds into overtime to give Quebec a 3-2 win against the Montreal Canadiens at the Forum in the fifth and deciding game of their first-round series in the Stanley Cup Playoffs. He scored an NHL career-high 28 goals in 1985-86 (a total he later matched in 1991-92), but dropped to 10 in 46 games in 1986-87 and was traded to the Washington Capitals on June 13, 1987.

Though Hunter averaged well over 200 penalty minutes in his first six seasons with Washington, he also averaged more than 21 goals during that span, finishing with an NHL career-best 79 points (20 goals, 59 assists) in 1992-93. He also scored seven goals in six playoff games against the New York Islanders in 1993 before making an errant pass that led to a series-clinching goal by New York's Pierre Turgeon; Hunter checked a celebrating Turgeon into the boards after the goal and was suspended by the NHL for 21 games of the 1993-94 season.

Hunter never scored more than 14 goals or finished with more than 46 points in any of his final six seasons with the Capitals. He was named captain of the Capitals before the 1994-95 season, played in the 1997 NHL All Star Game and was part of the first Washington team to advance to the Stanley Cup Final, in 1998, although the Detroit Red Wings swept the series. Hunter finished his NHL career by playing 12 games with the Colorado Avalanche (the former Nordiques, who had moved to Denver in 1995) after being traded on March 23, 1999.

The Capitals retired Hunter's No. 32 on March 11, 2000. He became part owner of London in the OHL in 2000 and was team president and coach beginning in 2001, with the exception of a 60-game stint as coach of the Capitals in 2011-12.

Hunter led London to the Memorial Cup in 2005 and 2016, and coached Canada to a first-place finish at the 2020 IIHF World Junior Championship.